Document EP 1 878 833 describes a treatment device of the above-specified type. When it is desired to treat a portion of soil with such a device, it is necessary to perform a first step of boring in order to form a tubular cavity in the soil. This first step is performed with the help of a distinct boring tool, which is then extracted from the borehole prior to inserting the treatment device. The tubular cavity may be in the form of a simple borehole. Another solution consists in introducing tubing into the soil and then boring within the tubing in order to make the cavity. In a second step, the treatment device is inserted inside the cavity and is moved along the cavity until its bottom end penetrates into the portion of soil that is to be treated. The mixer tool is then deployed, the shaft is set into rotation, and a fluid is injected simultaneously into the portion of soil via the bottom end of the shaft. The first step of making the tubular cavity requires the use of boring tools and occupies time, which as a result is not used for the actual operation of treating the soil. When the tubular cavity is defined by a tube, removing the tube constitutes a third step that is additional to the two preceding steps, thereby further reducing the productivity of the treatment method.